🧮 algebra

1. **State the problem:** Solve the equation $$\frac{1}{x^2 - x} + \frac{1}{x} = 1.$$\n\n2. **Rewrite the equation and identify the domain:** Note that $$x^2 - x = x(x-1),$$ so the

1. **Problem statement:** Given four functions A, B, C, and D with their graphs described, answer the following:

1. **State the problem:** Determine the domain of the function $$f(z) = \frac{z}{z-4}$$. 2. **Recall the domain rule for rational functions:** The domain includes all real numbers

1. The problem is to graph the function $$y=\frac{1}{3}x + 1$$ and find its domain and range. 2. The formula given is a linear function in slope-intercept form $$y=mx+b$$ where $$m

1. **Problem:** explain the fraction $\frac{2}{4}$ using a pie-style picture. 2. A fraction means **part of a whole**.

1. **State the problem:** Solve the equation $\sqrt{2x + 6} + 4 = x + 3$ for $x$. 2. **Isolate the square root:** Subtract 4 from both sides:

1. 题目：计算分数 $\frac{3}{4} + \frac{2}{5}$ 的值。 2. 公式和规则：

1. **State the problem:** Dakola purchased tickets costing 35.50 each plus a 7 handling charge, spending less than 150 in total. We need to find the greatest number of tickets she

1. **State the problem:** Caitlan has 50 to spend on canoeing. She must pay an 18 deposit plus 10.5 per hour. We want to find the greatest number of hours $x$ she can rent the cano

1. **Problem Statement:** Convert each improper fraction into a mixed number. 2. **Formula and Explanation:** An improper fraction has a numerator larger than the denominator. To c

1. **State the problem:** Find the area of a square with side length $\frac{2}{3}y$ cm. 2. **Formula for the area of a square:**

1. The problem asks who is correct about the first step in multiplying the expressions $\frac{7}{12} \left( \frac{1}{6}x - \frac{1}{3} + \frac{3}{4}x - \frac{5}{12} \right)$. Juan

1. **State the problem:** Simplify the expression $$2(5 + 3x) + (x + 10)$$. 2. **Use the distributive property:** Multiply 2 by each term inside the first parentheses.

1. **State the problem:** Solve for $x$ in the equation $3 - 14x = 17$. 2. **Isolate the term with $x$:** Subtract 3 from both sides to get the term with $x$ alone.

1. **State the problem:** We need to find the average rate of change of the function $f(x)$ on the interval $[-6, -4]$ by using the line segment connecting the points where $x = -6

1. **Stating the problem:** Risolvi la disequazione $$\frac{x+6}{x-3} \geq 0$$. 2. **Formula and rules:** Per risolvere disequazioni frazionarie, analizziamo il segno del numerator

1. **State the problem:** Solve the equation $$45 + 2x = 5x - 9$$ and prove that $$x = 18$$. 2. **Formula and rules:** To solve linear equations, we use properties of equality such

1. **State the problem:** Given the equation $$\frac{1}{3}x - 6 = 10$$, prove that $$x = 48$$. 2. **Show the formula and rules:** To solve for $$x$$, we use the Multiplication Prop

1. **Stating the problem:** We have a 3×3 grid where each cell contains expressions involving logarithms base 10 of numbers formed by digits in red and blue boxes.

1. **State the problem:** We need to fill in the boxes with digits 0 to 9 (each digit used once per blue box and once per red box) to make the logarithmic expressions true and incr

1. **State the problem:** Factorise fully the expression $$8ax - 14bx + 4ay - 7by$$. 2. **Identify common factors:** Group terms to find common factors: